CN1549207A - Method for filling closed area - Google Patents

Abstract

A method for filling a closed area. The closed area is surrounded by a closed path formed by a plurality of vertices. The method comprises the following steps. First, a path linked list is generated. The path linked list comprises a plurality of nodes, each node being used to record a vertex on the closed path or a plurality of intermediate points between vertices on the closed path. Next, a filling array linked list is generated based on the path linked list. The filling array linked list is used to record a plurality of filling line segments, the two end points of each filling line segment being located on the closed path, and these filling line segments being located within the closed area. Finally, the closed area is filled based on these filling line segments.

Description

Filling methods for closed areas

technical field

The invention relates to a filling method for a closed area, and in particular to a fast filling method for a closed area.

Background technique

Please refer to FIG. 1 , which is a flow chart of a traditional closed area filling method. First, the coordinates of the vertices on the path are obtained, as shown in step 110 . These vertices are, for example, those shown in FIG. 2 . Then, find the smallest rectangle containing all vertices, as shown in step 120 . Next, open up an area in the memory corresponding to the area of the smallest rectangle where the vertices are distributed (one byte corresponds to one pixel), as shown in step 130 . Then, in the memory area, all points outside the closed area, all points inside the closed area, vertices of paths, hypotenuses (including vertical edges, excluding vertices) and horizontal edges (excluding vertices) are represented by different Value to identify, as shown in step 140. Next, scan line by line and point by point, and judge whether it is the end point of the filled line segment according to the position of the current point and the value marked by the current point, as shown in step 150 . Finally, the closed area is filled according to the value of the end point of the filled line segment obtained above, as shown in step 160 .

Take a closed path composed of 100 vertices as an example, and these vertices are distributed on an area whose length and width are 100×100 (unit: pixel). In the third step of the old algorithm, when judging whether a point is inside a closed area, it is necessary to compare the coordinates of this point (a total of 100×100 points) with the coordinates of all vertices on the path (a total of 100 vertices) Coordinates are compared to see if they are vertices of the path. For this item alone, it is necessary to judge about (100×100)×100 times, that is, 1,000,000 times. Most of the time is consumed in such operations. In step 150, when judging whether the current point is the end point of the filled line segment, it is necessary to judge the 100×100 points one by one, and the computation load is relatively large.

In step 130, an area (100×100 byte) needs to be opened in the memory corresponding to the area where the vertices are distributed and whose length and width are 100×100 (unit: pixel). When the area where vertices are distributed is large, it will take up a lot of memory space.

Contents of the invention

In view of this, the object of the present invention is to provide a fast filling method for closed areas.

According to the object of the present invention, a method of filling an enclosed area is proposed. A closed region is enclosed in a closed path formed by multiple vertices. The method includes the following steps. First, generate a path linked list. The path link list includes multiple nodes, and each node is used to record vertices on the closed path or multiple intermediate points between vertices on the closed path. Next, a filled array linked list is generated according to the path linked list. The filling array linked list is used to record a plurality of filling line segments, the two ends of each filling line segment are located on the closed path, and these filling line segments are located in the closed area. Finally, fill this closed area according to these filled line segments.

According to the filling method of the present invention, it has the following advantages: 1. reduce the amount of computation:

a. Instead of judging all the pixels in the closed area point by point as in the traditional method, only the pixels on the closed path are judged, so the amount of computation can be reduced. b. There are no complex multiplication and division calculations, and most of them are simple numerical comparisons, so the amount of calculation can be reduced. 2. Reduce memory requirements: The traditional method requires a block of memory corresponding to all the pixels of the smallest rectangle surrounding all vertices, so more memory is required. However, this method only needs to route the linked list, fill the array linked list, etc., and requires less memory.

Description of drawings

In order to make the above-mentioned purposes, features, and advantages of the present invention more comprehensible, a preferred embodiment is specifically cited below, and in conjunction with the accompanying drawings, the detailed description is as follows:

FIG. 1 shows a flow chart for a traditional closed area filling method.

Fig. 2 shows a graph of distribution of multiple vertices on a plane.

Fig. 3 shows a flowchart of a method for filling a closed area according to a preferred embodiment of the present invention.

FIG. 4A shows a flowchart for determining the line label of a vertex.

FIG. 4B shows a flowchart for determining the point label of a vertex.

FIG. 4C shows a flowchart of a method for determining an endpoint flag of a vertex.

4D and 4E show the flowchart of the method for generating the path link list.

FIG. 5A is a schematic diagram of pixels linked by the path list P.

FIG. 5B shows the content in the path list P.

6A and 6B show a flowchart of a method for generating a filled array linked list.

FIG. 7 shows the contents of the filled array linked list generated according to the flow in FIGS. 6A and 6B.

Fig. 8 shows a schematic diagram of the closed area after filling.

Detailed ways

Fig. 2 shows a graph of distribution of multiple vertices on a plane. The coordinates of vertices (0) to (10) are (6, 0), (2, 4), (5, 4), (0, 8), (5, 8), (5, 12), ( 7,12), (7,8), (12,8), (7,4) and (10,4). The last vertex (11) is also vertex (0). These vertices enclose a closed path, and the closed path encloses a closed area. The following description will take these vertices in Fig. 2 as examples. Fig. 3 shows a flowchart of a method for filling a closed area according to a preferred embodiment of the present invention. These vertices are first received, as shown in step 300 . The coordinates of these vertices are recorded sequentially in a vertex array, and the last vertex of the path is the first vertex. Then, calculate all intermediate points between the vertices on the closed path according to these vertices, and store these vertices and intermediate points in the path linked list (linked list) P according to the order of the closed path, as shown in step 400 . Then, the filled array linked list G is obtained according to the path linked list P, as shown in step 500 . Filling the array linked list G is to record the points at both ends of the horizontal line segment that needs to be filled. Finally, the closed area is filled according to the filling array linked list G, as shown in step 600 .

In step 400, the method of generating the path link list P is described as follows. First, the attributes of each vertex are determined, as shown in the flow charts in FIGS. 4A to 4C. Then, calculate all intermediate points between the vertices on the closed path and store these vertices and intermediate points in the path list P according to the order of the closed path, as shown in the flowcharts of Figures 4D and 4E.

Each vertex has an ordinate x and an abscissa y, and has different attributes depending on the relative position of the vertex and other vertices, represented by a line flag (flag) F1, a point flag Fp, and an endpoint flag Fe. The current vertex is represented by vertex (r), the previous vertex is represented by vertex (r-1), and the next vertex is represented by vertex (r+1). If the current vertex (r) is the first one, that is, vertex (0), then vertex (r-1) is vertex (10); similarly, if the current vertex (r) is vertex (11), then vertex (r +1) for vertex (1). r is a positive integer.

FIG. 4A shows a flowchart for determining the line label of a vertex. The line flag F1 is determined to be horizontal, vertical or inclined according to the line segment formed by the current vertex and the previous vertex. First, it is checked whether the ordinate y(r) of the current vertex (r) is equal to the ordinate y(r-1) of the previous vertex (r-1), as shown in step 310 . If so, it means that the line segment between the current vertex (r) and the previous vertex (r-1) is horizontal, then mark the line flag F1 of the current vertex (r) as horizontal, as shown in step 312, eg vertex (2). Otherwise, check whether the abscissa x(r) of the current vertex (r) is equal to the abscissa x(r-1) of the previous vertex (r-1), as shown in step 314 . If yes, the line flag F1 of the current vertex (r) is marked as vertical, as shown in step 316, eg vertex (5). If not, the abscissa x(r) and y(r) of the vertex (r) are respectively related to the abscissa x(r-1) and y(r-1) of the previous vertex (r-1) If not, mark the line flag F1 of the current vertex (r) as inclined, as shown in step 318, for example, vertex (1).

FIG. 4B shows a flowchart for determining the point label of a vertex. The point flag Fp is determined as type A, type C, type L1 or type L2 according to the relative positions of the current vertex (r) and the previous vertex (r-1) and the next vertex (r+1). First check whether the ordinate y(r) of the current vertex (r) is greater than the ordinate y(r-1) of the previous vertex (r-1) and the ordinate y(r+) of the next vertex (r+1) at the same time 1), as shown in step 320. If so, the point flag Fp of the current vertex (r) is type A, such as vertex (0). If not, check whether the ordinate y(r) of the current vertex (r) is smaller than the ordinate y(r-1) of the previous vertex (r-1) and the ordinate y(r) of the next vertex (r+1) at the same time r+1), as shown in step 324. If yes, then the point flag Fp of the current vertex (r) is type A, as shown in step 322 . If not, check whether the ordinate y of the current vertex (r) is between the ordinate y(r-1) of the previous vertex (r-1) and the ordinate y(r+1) of the next vertex (r+1) ), as shown in step 326. If so, the point flag Fp of the current vertex (r) is C type, as shown in step 328 . If not, it means that the ordinate of the current vertex (r) is the same as the ordinate of the previous vertex (r-1) or the next vertex (r+1). At this point, check whether the ordinate y(r) of the current vertex (r) is the same as the ordinate y(r-1) of the previous vertex (r-1), as shown in step 330 . If so, it means that the line segment between the current vertex (r) and the previous vertex (r-1) is horizontal, and proceeds to step 332; otherwise, it represents that the line segment between the current vertex (r) and the next vertex (r+1) is horizontal, and proceeds to step 334 . In step 332, it is checked whether the abscissa x of the current vertex (r) is greater than the abscissa x of the previous vertex (r-1). If so, then the point mark Fp of vertex (r) is L2 type, as shown in step 338, such as vertex (2); if not, then the point mark Fp of current vertex (r) is L1 type, as shown in step 336. In step 334, it is checked whether the abscissa x(r) of the current vertex (r) is greater than the abscissa x(r+1) of the next vertex (r+1). If so, then the point flag Fp of the current vertex (r) is L2 type, as shown in step 338;

FIG. 4C shows a flowchart of a method for determining an endpoint flag of a vertex. In step 340, check three conditions, if one of these three conditions is set up, then represent that the endpoint mark Fe of vertex (r) is true (step 342), otherwise represent that the endpoint mark Fe of vertex (r) is false (step 344). The first condition is: the ordinate y(r) of the current vertex (r) is less than the ordinate y(r+1) of the next vertex (r+1), and greater than or equal to the ordinate of the previous vertex (r-1) y(r-1). The second condition is: the ordinate y(r) of the current vertex (r) is less than the ordinate y(r-1) of the previous vertex (r-1), and greater than or equal to the ordinate of the next vertex (r+1) y(r+1). The third condition is: the point flag Fp of the current vertex (r) is type A or type C. If the endpoint flag Fe is true, it means that the vertex (r) is the endpoint of the filled line segment. Repeat the process shown in FIGS. 4A to 4C until all vertices have obtained their line markers F1 , point markers Fp and endpoint markers Fe.

Next, calculate all intermediate points between vertices on the closed path, and store these vertices and intermediate points in the path list P in the order of the closed path. 4D and 4E show the flowchart of the method for generating the path link list. The method of obtaining the intermediate point and the order of inserting into the path list P are determined according to the line flag F1 of the current vertex (r). In step 350, it is judged whether the line mark F1 of the current vertex (r) is horizontal, and if so, step 352 is executed. In step 354, it is judged whether the line flag F1 of the current vertex (r) is vertical, and if so, execute steps 356-362. If the judgment results of steps 350 and 354 are both negative, then the line flag F1 of the current vertex (r) is inclined, and steps 363-368 are executed.

If the line flag F1 of the current vertex (r) is horizontal, the current vertex (r) is inserted into the end of the path list P (step 352), and step 370 is executed to determine whether the current vertex (r) is inserted into the path list P. That is to say, if the line segment between the vertex (r) and the vertex (r-1) is horizontal, the intermediate point will not be recorded in the path list P.

If the line mark F1 of current vertex (r) is vertical, at first judge in step 356: Whether the ordinate y (r) of current vertex (r) is greater than the ordinate y (r-1) of previous vertex (r-1) ), that is, the vertex (r) is below the vertex (r-1), and the ordinate y(r) of the current vertex (r) and the ordinate y(r-1) of the previous vertex (r-1) The difference is greater than 2, that is, there is an intermediate point between the vertex (r) and the vertex (r-1). If yes, then sequentially insert the intermediate points between the vertex (r-1) and the vertex (r) into the path list P, that is, in the order of increasing ordinate (step 358); otherwise, go to step 360. Judging in step 360: whether the ordinate y(r) of the current vertex (r) is less than the ordinate y(r-1) of the previous vertex (r-1), that is, the vertex (r) is at the vertex (r-1) ), and the difference between the vertical coordinate y(r) of the current vertex (r) and the vertical coordinate y(r-1) of the previous vertex (r-1) is greater than 2, that is, the difference between the vertex (r) and the vertex (r -1) There is an intermediate point between them. If so, insert the intermediate points between the vertex (r-1) and the vertex (r) into the path list P in order, that is, in the order of decreasing ordinate (step 358); otherwise, go to step 370.

If the line mark F1 of current vertex (r) is inclined, at first judge in step 363: Whether the ordinate y (r) of current vertex (r) is greater than the ordinate y (r-1) of previous vertex (r-1) ), that is, the vertex (r) is below the vertex (r-1), and the ordinate y(r) of the current vertex (r) and the ordinate y(r-1) of the previous vertex (r-1) The difference is greater than 2, that is, there is an intermediate point between the vertex (r) and the vertex (r-1). If so, insert the intermediate points between the vertex (r-1) and the vertex (r) into the path list P in order, that is, in the order of increasing ordinate (step 364); otherwise, go to step 366. These intermediary points are obtained according to the straight line equation of the vertex (r) and the vertex (r-1). In step 366, it is judged: whether the ordinate y (r) of the current vertex (r) is less than the ordinate y (r-1) of the previous vertex (r-1), that is, the vertex (r) is at the vertex (r-1) ), and the difference between the vertical coordinate y(r) of the current vertex (r) and the vertical coordinate y(r-1) of the previous vertex (r-1) is greater than 2, that is, the difference between the vertex (r) and the vertex (r -1) There is an intermediate point between them. If so, insert the intermediate points between the vertex (r-1) and the vertex (r) into the path list P in order, that is, in descending order of the ordinate (step 368); otherwise, go to step 370. These intermediary points are obtained according to the straight line equation of the vertex (r) and the vertex (r-1). In step 370, if the current vertex (r) is not the last vertex of the path, insert the vertex (r) into the end of the path list P. Repeat the method shown in Figures 4D and 4E until all vertices and intermediate points have been stored in the path list P in the order of closed paths.

FIG. 5A is a schematic diagram of pixels linked by the path list P. In addition to the vertices, the intermediate point between the vertices is also calculated, and the intermediate point between the two vertices on the horizontal line is not recorded, for example, there is no intermediate point recorded between the vertex (1) and the vertex (2). FIG. 5B shows the content in the path list P. Each element in the path list P corresponds to a vertex or an intermediate point, and each element includes an abscissa x, a ordinate y, an index index, a point symbol Fp, an endpoint symbol Fe and an index next. The index index is used to record the order of each vertex, and the index index of the intermediate point is -1, for example, the index index of the vertex (0) is 0. The point markers Fp of the intermediate points are all C-type. If the endpoint flag Fe is true, it will be represented by 1 in the path list P, otherwise it will be represented by 0. The indicator next is used to point to the next node. The elements are linked sequentially in the order of the closed path.

Next, the method for generating the filled array linked list in step 500 will be described in detail. First, apply for a filled array list G according to the height h of the closed path. In this example, h is 13. Each array filling the array linked list G corresponds to a linked list, and a linked list corresponds to pixels in the same column. For example, G[0] is the pixel corresponding to the vertical coordinate y=0, G[1] is the pixel corresponding to the vertical coordinate y=1, . . . , G[12] is the pixel corresponding to the vertical coordinate y=12. In addition, the linked list pointed to by G[13] is used to record all horizontal lines on the closed path. The linked list pointed to by each G[] includes the two endpoints of the filled line segment. The closed area enclosed by these vertices can be filled according to the filled line segment. 6A and 6B show a flowchart of a method for generating a filled array linked list G. FIG. All vertices and intermediary points on the closed path, that is, each node of the path list P, are filled in the filling array list G in this way in sequence. First check whether the node is an intermediary point (step 512), if so, write this node into the corresponding filling array linked list G[y] (step 514) according to its ordinate y, if not, indicate that this node is a vertex. In step 520, check whether the point flag Fp of this vertex is type A, and if so, write the corresponding filling array linked list G[y] twice according to its ordinate y. If the point flag Fp is type A, such as the vertex A in Figure 2, it means that the same horizontal line has only this point, so writing it twice means that the starting point and the ending point of this filled line segment are the same point. Then check whether the point flag Fp of the vertex is L1 or L2 type (step 530), if so, it means that this vertex is located on the horizontal line segment of the closed path, and proceeds to step 532, otherwise proceeds to step 540. In step 532, this vertex is written into the filled array linked list G[h], and then the endpoint flag Fe of this vertex in the filled array linked list G[h] is changed to true (step 534). Then check whether the endpoint flag Fe of this vertex in the path linked list P is true (step 536), if then write this vertex into the corresponding filling array linked list G[y] (step 538) according to its ordinate y. If the point flag Fp of the vertex is C type, write the vertex into the corresponding filled array linked list G[y] according to its ordinate y (step 540).

FIG. 7 shows the content of the filled array linked list generated according to the process of FIGS. 6A and 6B . The filling array linked list G[0] is the filling line segment (6,0)(6,0) corresponding to y=0, and the filling array linked list G[1] is the filling line segment (5,1)(7) corresponding to y=1 , 1), the filling array linked list G[2] is the filling line segment (4,2)(8,2) corresponding to y=2, and the filling array linked list G[3] is the filling line segment (3, 2) corresponding to y=3 3) (9, 3), ..., the filling array linked list G[11] is the filling line segment (5, 11) (7, 11) corresponding to y=11. The filling array linked list G[12] is a filling line segment corresponding to y=12, and there is no filling line segment here. The filled array linked list G[h], that is, G[13], is a horizontal linked list used to record all horizontal lines (2, 4) (5, 4), (0, 8) (5, 8), (5,12)(7,12)(7,8)(12,8) and (7,4)(10,4).

Finally, the closed area is filled according to the filled array linked list G. Please refer to FIG. 8 , which is a schematic diagram of the closed area after filling. The end point coordinates of the filled line segments can be obtained according to the filled array linked list G, and the end points of each filled line segment are connected with a specific color, and all the filled line segments and the horizontal line segments on the closed path are colored, and the closed area is filled.

The method for filling the enclosed area disclosed in the above embodiments of the present invention has the following advantages:

1. Reduce the amount of computation:

a. Instead of judging all the pixels in the closed area point by point as in the traditional method, only the pixels on the closed path are judged, so the amount of computation can be reduced.

b. There are no complex multiplication and division calculations, and most of them are simple numerical comparisons, so the amount of calculation can be reduced.

2. Reduce memory requirements: The traditional method requires a block of memory corresponding to all the pixels of the smallest rectangle surrounding all vertices, so more memory is required. However, this method only needs to route the linked list, fill the array linked list, etc., and requires less memory.

In summary, although the present invention is disclosed according to the above-mentioned preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can change or improve without departing from the spirit and scope of the present invention. Therefore, the present invention The scope of protection is subject to what is described in the claims.

Claims (22)

1. A filling method of a closed area, the closed area is surrounded by a closed path formed by a plurality of vertices, according to the order on the closed path, each of the vertices has a previous vertex and a subsequent vertex, the method includes: generating a path link list, the path link list includes a plurality of nodes, and each node is used to record one of the plurality of intermediate points between these vertices on the closed path and each of these vertices on the closed path; generating a filled array linked list according to the path linked list, for recording a plurality of filled line segments, the two ends of each of these filled line segments are located on the closed path, and these filled line segments are located in the closed area; and The closed area is filled according to these filled line segments. 2. The filling method according to claim 1, wherein the step of generating the path linked list comprises: a1. According to the relative position of the previous vertex and the vertex, the line mark of the vertex is determined to be one of horizontal, vertical and inclined; a2. If there is an intermediate point between the vertex and the previous vertex, inserting the intermediate point between the vertex and the previous vertex into the path list according to the line marker of the vertex; and a3. If the vertex is not the last vertex on the closed path, insert the vertex at the end of the path list. 3. The filling method as claimed in claim 2, wherein in step a2, if the line mark of the vertex is horizontal, the intermediate points between the vertex and the previous vertex are not recorded. 4. The filling method according to claim 2, wherein in step a2, if the line mark of the vertex is vertical, and the ordinate of the vertex is greater than the ordinate of the previous vertex, the previous vertex and the vertex These intermediary points between the vertices are inserted into the tail of the path list in the order of increasing ordinates. 5. The filling method according to claim 2, wherein in step a2, if the line mark of the vertex is vertical, and the ordinate of the vertex is smaller than the ordinate of the previous vertex, and the vertex and the previous vertex If there are intermediary points between a vertex, these intermediary points between the previous vertex and this vertex are inserted into the end of the path list in descending order of their ordinates. 6. The filling method according to claim 2, wherein in step a2, if the line mark of the vertex is inclined, and the ordinate of the vertex is greater than the ordinate of the previous vertex, then the previous vertex and These intermediary points between the vertices are inserted into the tail of the path list in the order of their ordinates increasing. 7. The filling method according to claim 2, wherein in step a2, if the line mark of the vertex is inclined, and the ordinate of the vertex is smaller than the ordinate of the previous vertex, then the previous vertex and These intermediary points between the vertices are inserted into the tail of the path list in descending order of their ordinates. 8. The filling method as claimed in claim 7, wherein in step a2, the intermediary points are sequentially obtained through linear equations of the vertex and the previous vertex. 9. The filling method according to claim 2, wherein in step a1, if the abscissa of the vertex is equal to the abscissa of the previous vertex, the line mark of the vertex is horizontal. 10. The filling method as claimed in claim 2, wherein in step a1, if the ordinate of the vertex is equal to the ordinate of the previous vertex, the line flag of the vertex is vertical. 11. The filling method according to claim 2, wherein in step a1, if the abscissa of the vertex is not equal to the abscissa of the previous vertex, and the ordinate of the vertex is the same as that of the previous vertex If the ordinates are not equal, then the line marker for the vertex is oblique. 12. The filling method according to claim 1, wherein the filling array linked list has a plurality of line segment linked lists, and each of the line segment linked lists is used to record one of the filled line segments. 13. The filling method as claimed in claim 12, wherein the filling lines are horizontal. 14. The filling method according to claim 13, wherein in the step of generating the filling array linked list, if the node of the path linked list is the intermediate point, then the intermediate point is recorded to the corresponding intermediate point according to the ordinate of the intermediate point The line segment linked list. 15. The filling method according to claim 13, wherein in the step of generating the filling array linked list, if the node of the path linked list is the vertex, and the ordinate of the vertex is greater than the ordinate of the previous vertex and the ordinate of the latter vertex, then record the vertex in the corresponding line segment linked list twice according to the ordinate of the vertex. 16. The filling method according to claim 13, wherein in the step of generating the filled array linked list, if the node of the path linked list is the vertex, and the ordinate of the vertex is smaller than the ordinate of the previous vertex and the ordinate of the latter vertex, then record the vertex in the corresponding line segment linked list twice according to the ordinate of the vertex. 17. The filling method of claim 13, wherein the filling array linked list further comprises a horizontal linked list for recording at least one horizontal line segment on the closed path. 18. The filling method according to claim 17, wherein in the step of generating the filled array linked list, if the node of the path linked list is the vertex, and the vertex forms one of the previous vertex and the next vertex For the horizontal line segment, record the vertex into the horizontal linked list of the filled array linked list. 19. The filling method according to claim 17, in the step of generating the filled array linked list, if the node of the path linked list is the vertex, and the vertex forms the horizontal line segment with the previous vertex, then according to the vertex The vertical coordinate of the vertex is recorded in the corresponding line segment linked list. 20. The filling method according to claim 13, in the step of generating the filled array linked list, if the node of the path linked list is the vertex, and the ordinate of the vertex is between the previous vertex (r-1 ) and the ordinate of the next vertex, the vertex is recorded in the corresponding line segment linked list according to the ordinate of the vertex. 21. The filling method according to claim 13, wherein in the step of filling the closed area, the filling line segments recorded in the line segment link lists are respectively filled. 22. The filling method as claimed in claim 17, wherein in the step of filling the enclosed area, the filling line segments recorded in the line segment link list and the at least one horizontal line segment recorded in the horizontal link list are respectively filled.

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